Problem: What do the following two equations represent? $-3x+5y = 2$ $3x-5y = 0$
Answer: Putting the first equation in $y = mx + b$ form gives: $-3x+5y = 2$ $5y = 3x+2$ $y = \dfrac{3}{5}x + \dfrac{2}{5}$ Putting the second equation in $y = mx + b$ form gives: $3x-5y = 0$ $-5y = -3x$ $y = \dfrac{3}{5}x + 0$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.